OFFSET
1,2
COMMENTS
It is conjectured that this is a permutation of the positive integers, along with any Seelmann sequence in which a(n+1) = M*a(n) if the divide by 2 rule cannot be applied, for any integer M>1 and not of the form M = 2^N. [Corrected by Charlie Neder, Feb 06 2019]
Reminiscent of the 3x+1 or Collatz problem, cf. A006577. - N. J. A. Sloane, Feb 09 2016
The Reddit link contains what is claimed to be a proof that this sequence is a permutation. I don't know if it has been checked. - N. J. A. Sloane, Feb 11 2016
LINKS
Peter Kagey, Table of n, a(n) for n = 1..10000
David Seelmann, Proving a sequence of integers reaches every integer, Posting to Reddit Web Site, Jan 09 2016
MATHEMATICA
a[1]=1; a[n_] := a[n] = Module[{an1, an}, an1 = a[n-1]; an = If[EvenQ[an1], an1/2, (an1+1)/2]; If[FreeQ[Array[a, n-1], an], an, 3*a[n-1]]]; Array[a, 100] (* Jean-François Alcover, Feb 27 2016 *)
Fold[Append[#1, If[FreeQ[#1, #3], #3, 3 #1[[-1]]]] & @@ {#1, #2, Ceiling[#1[[-1]]/2]} &, {1}, Range@ 63] (* Michael De Vlieger, Jan 13 2018 *)
CROSSREFS
KEYWORD
nonn,nice
AUTHOR
Peter Kagey, Feb 09 2016, based on a posting by David Seelmann to the Reddit web site.
EXTENSIONS
Title corrected by Charlie Neder, Feb 06 2019
STATUS
approved